Second-Order Path Kernel Interpolation Formulas in Machine Learning
Understanding how training data shape neural network predictions is a central problem in modern learning theory. In 2020, Pedro Domingos proposed an interpolation formula valid for every model learned by deterministic gradient descent. It expresses the model's prediction as an integral, along the optimization path, of a data-dependent kernel that aligns the model's gradients at the test and training data. Such a first-order characterization remains valid for models trained with batch-based stochastic optimization. In this paper, we develop second-order forms of these interpolation formulas. We show that the leading path-kernel interpolation is supplemented by a curvature-weighted interpol...
| Authors | Jin Guo, Roy Y. He, Jean-Michel Morel |
|---|---|
| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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